# HG changeset patch
# User wenzelm
# Date 1376832672 -7200
# Node ID acc495621d728d6401fc59b736e80e4384b6d3b2
# Parent  1958a5e65ea59e157725eafa241693febb37c3d8
prefer plain subscript;

diff -r 1958a5e65ea5 -r acc495621d72 src/HOL/Decision_Procs/Dense_Linear_Order.thy
--- a/src/HOL/Decision_Procs/Dense_Linear_Order.thy	Sun Aug 18 15:10:18 2013 +0200
+++ b/src/HOL/Decision_Procs/Dense_Linear_Order.thy	Sun Aug 18 15:31:12 2013 +0200
@@ -34,7 +34,7 @@
 lemma gather_start [no_atp]: "(\<exists>x. P x) \<equiv> (\<exists>x. (\<forall>y \<in> {}. y < x) \<and> (\<forall>y\<in> {}. x < y) \<and> P x)" 
   by simp
 
-text{* Theorems for @{text "\<exists>z. \<forall>x. x < z \<longrightarrow> (P x \<longleftrightarrow> P\<^bsub>-\<infinity>\<^esub>)"}*}
+text{* Theorems for @{text "\<exists>z. \<forall>x. x < z \<longrightarrow> (P x \<longleftrightarrow> P\<^sub>-\<^sub>\<infinity>)"}*}
 lemma minf_lt[no_atp]:  "\<exists>z . \<forall>x. x < z \<longrightarrow> (x < t \<longleftrightarrow> True)" by auto
 lemma minf_gt[no_atp]: "\<exists>z . \<forall>x. x < z \<longrightarrow>  (t < x \<longleftrightarrow>  False)"
   by (simp add: not_less) (rule exI[where x="t"], auto simp add: less_le)
@@ -46,7 +46,7 @@
 lemma minf_neq[no_atp]: "\<exists>z. \<forall>x. x < z \<longrightarrow> (x \<noteq> t \<longleftrightarrow> True)" by auto
 lemma minf_P[no_atp]: "\<exists>z. \<forall>x. x < z \<longrightarrow> (P \<longleftrightarrow> P)" by blast
 
-text{* Theorems for @{text "\<exists>z. \<forall>x. x < z \<longrightarrow> (P x \<longleftrightarrow> P\<^bsub>+\<infinity>\<^esub>)"}*}
+text{* Theorems for @{text "\<exists>z. \<forall>x. x < z \<longrightarrow> (P x \<longleftrightarrow> P\<^sub>+\<^sub>\<infinity>)"}*}
 lemma pinf_gt[no_atp]:  "\<exists>z. \<forall>x. z < x \<longrightarrow> (t < x \<longleftrightarrow> True)" by auto
 lemma pinf_lt[no_atp]: "\<exists>z. \<forall>x. z < x \<longrightarrow>  (x < t \<longleftrightarrow>  False)"
   by (simp add: not_less) (rule exI[where x="t"], auto simp add: less_le)
@@ -351,7 +351,7 @@
 
 lemma ge_ex[no_atp]: "\<exists>y. x \<sqsubseteq> y" using gt_ex by auto
 
-text {* Theorems for @{text "\<exists>z. \<forall>x. z \<sqsubset> x \<longrightarrow> (P x \<longleftrightarrow> P\<^bsub>+\<infinity>\<^esub>)"} *}
+text {* Theorems for @{text "\<exists>z. \<forall>x. z \<sqsubset> x \<longrightarrow> (P x \<longleftrightarrow> P\<^sub>+\<^sub>\<infinity>)"} *}
 lemma pinf_conj[no_atp]:
   assumes ex1: "\<exists>z1. \<forall>x. z1 \<sqsubset> x \<longrightarrow> (P1 x \<longleftrightarrow> P1')"
   and ex2: "\<exists>z2. \<forall>x. z2 \<sqsubset> x \<longrightarrow> (P2 x \<longleftrightarrow> P2')"
@@ -402,7 +402,7 @@
 lemma le_ex[no_atp]: "\<exists>y. y \<sqsubseteq> x" using lt_ex by auto
 
 
-text {* Theorems for @{text "\<exists>z. \<forall>x. x \<sqsubset> z \<longrightarrow> (P x \<longleftrightarrow> P\<^bsub>-\<infinity>\<^esub>)"} *}
+text {* Theorems for @{text "\<exists>z. \<forall>x. x \<sqsubset> z \<longrightarrow> (P x \<longleftrightarrow> P\<^sub>-\<^sub>\<infinity>)"} *}
 lemma minf_conj[no_atp]:
   assumes ex1: "\<exists>z1. \<forall>x. x \<sqsubset> z1 \<longrightarrow> (P1 x \<longleftrightarrow> P1')"
     and ex2: "\<exists>z2. \<forall>x. x \<sqsubset> z2 \<longrightarrow> (P2 x \<longleftrightarrow> P2')"
diff -r 1958a5e65ea5 -r acc495621d72 src/HOL/Predicate_Compile_Examples/Specialisation_Examples.thy
--- a/src/HOL/Predicate_Compile_Examples/Specialisation_Examples.thy	Sun Aug 18 15:10:18 2013 +0200
+++ b/src/HOL/Predicate_Compile_Examples/Specialisation_Examples.thy	Sun Aug 18 15:31:12 2013 +0200
@@ -194,35 +194,35 @@
 | "\<down>\<^sub>e (Suc n) k \<Gamma> = \<down>\<^sub>e n k (\<Gamma>[k \<mapsto>\<^sub>\<tau> Top]\<^sub>e)"
 
 inductive
-  well_formed :: "env \<Rightarrow> type \<Rightarrow> bool"  ("_ \<turnstile>\<^bsub>wf\<^esub> _" [50, 50] 50)
+  well_formed :: "env \<Rightarrow> type \<Rightarrow> bool"  ("_ \<turnstile>\<^sub>w\<^sub>f _" [50, 50] 50)
 where
-  wf_TVar: "\<Gamma>\<langle>i\<rangle> = \<lfloor>TVarB T\<rfloor> \<Longrightarrow> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> TVar i"
-| wf_Top: "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> Top"
-| wf_arrow: "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> T \<Longrightarrow> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> U \<Longrightarrow> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> T \<rightarrow> U"
-| wf_all: "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> T \<Longrightarrow> TVarB T \<Colon> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> U \<Longrightarrow> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> (\<forall><:T. U)"
+  wf_TVar: "\<Gamma>\<langle>i\<rangle> = \<lfloor>TVarB T\<rfloor> \<Longrightarrow> \<Gamma> \<turnstile>\<^sub>w\<^sub>f TVar i"
+| wf_Top: "\<Gamma> \<turnstile>\<^sub>w\<^sub>f Top"
+| wf_arrow: "\<Gamma> \<turnstile>\<^sub>w\<^sub>f T \<Longrightarrow> \<Gamma> \<turnstile>\<^sub>w\<^sub>f U \<Longrightarrow> \<Gamma> \<turnstile>\<^sub>w\<^sub>f T \<rightarrow> U"
+| wf_all: "\<Gamma> \<turnstile>\<^sub>w\<^sub>f T \<Longrightarrow> TVarB T \<Colon> \<Gamma> \<turnstile>\<^sub>w\<^sub>f U \<Longrightarrow> \<Gamma> \<turnstile>\<^sub>w\<^sub>f (\<forall><:T. U)"
 
 inductive
-  well_formedE :: "env \<Rightarrow> bool"  ("_ \<turnstile>\<^bsub>wf\<^esub>" [50] 50)
-  and well_formedB :: "env \<Rightarrow> binding \<Rightarrow> bool"  ("_ \<turnstile>\<^bsub>wfB\<^esub> _" [50, 50] 50)
+  well_formedE :: "env \<Rightarrow> bool"  ("_ \<turnstile>\<^sub>w\<^sub>f" [50] 50)
+  and well_formedB :: "env \<Rightarrow> binding \<Rightarrow> bool"  ("_ \<turnstile>\<^sub>w\<^sub>f\<^sub>B _" [50, 50] 50)
 where
-  "\<Gamma> \<turnstile>\<^bsub>wfB\<^esub> B \<equiv> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> type_ofB B"
-| wf_Nil: "[] \<turnstile>\<^bsub>wf\<^esub>"
-| wf_Cons: "\<Gamma> \<turnstile>\<^bsub>wfB\<^esub> B \<Longrightarrow> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> \<Longrightarrow> B \<Colon> \<Gamma> \<turnstile>\<^bsub>wf\<^esub>"
+  "\<Gamma> \<turnstile>\<^sub>w\<^sub>f\<^sub>B B \<equiv> \<Gamma> \<turnstile>\<^sub>w\<^sub>f type_ofB B"
+| wf_Nil: "[] \<turnstile>\<^sub>w\<^sub>f"
+| wf_Cons: "\<Gamma> \<turnstile>\<^sub>w\<^sub>f\<^sub>B B \<Longrightarrow> \<Gamma> \<turnstile>\<^sub>w\<^sub>f \<Longrightarrow> B \<Colon> \<Gamma> \<turnstile>\<^sub>w\<^sub>f"
 
 inductive_cases well_formed_cases:
-  "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> TVar i"
-  "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> Top"
-  "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> T \<rightarrow> U"
-  "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> (\<forall><:T. U)"
+  "\<Gamma> \<turnstile>\<^sub>w\<^sub>f TVar i"
+  "\<Gamma> \<turnstile>\<^sub>w\<^sub>f Top"
+  "\<Gamma> \<turnstile>\<^sub>w\<^sub>f T \<rightarrow> U"
+  "\<Gamma> \<turnstile>\<^sub>w\<^sub>f (\<forall><:T. U)"
 
 inductive_cases well_formedE_cases:
-  "B \<Colon> \<Gamma> \<turnstile>\<^bsub>wf\<^esub>"
+  "B \<Colon> \<Gamma> \<turnstile>\<^sub>w\<^sub>f"
 
 inductive
   subtyping :: "env \<Rightarrow> type \<Rightarrow> type \<Rightarrow> bool"  ("_ \<turnstile> _ <: _" [50, 50, 50] 50)
 where
-  SA_Top: "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> \<Longrightarrow> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> S \<Longrightarrow> \<Gamma> \<turnstile> S <: Top"
-| SA_refl_TVar: "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> \<Longrightarrow> \<Gamma> \<turnstile>\<^bsub>wf\<^esub> TVar i \<Longrightarrow> \<Gamma> \<turnstile> TVar i <: TVar i"
+  SA_Top: "\<Gamma> \<turnstile>\<^sub>w\<^sub>f \<Longrightarrow> \<Gamma> \<turnstile>\<^sub>w\<^sub>f S \<Longrightarrow> \<Gamma> \<turnstile> S <: Top"
+| SA_refl_TVar: "\<Gamma> \<turnstile>\<^sub>w\<^sub>f \<Longrightarrow> \<Gamma> \<turnstile>\<^sub>w\<^sub>f TVar i \<Longrightarrow> \<Gamma> \<turnstile> TVar i <: TVar i"
 | SA_trans_TVar: "\<Gamma>\<langle>i\<rangle> = \<lfloor>TVarB U\<rfloor> \<Longrightarrow>
     \<Gamma> \<turnstile> \<up>\<^sub>\<tau> (Suc i) 0 U <: T \<Longrightarrow> \<Gamma> \<turnstile> TVar i <: T"
 | SA_arrow: "\<Gamma> \<turnstile> T\<^sub>1 <: S\<^sub>1 \<Longrightarrow> \<Gamma> \<turnstile> S\<^sub>2 <: T\<^sub>2 \<Longrightarrow> \<Gamma> \<turnstile> S\<^sub>1 \<rightarrow> S\<^sub>2 <: T\<^sub>1 \<rightarrow> T\<^sub>2"
@@ -232,7 +232,7 @@
 inductive
   typing :: "env \<Rightarrow> trm \<Rightarrow> type \<Rightarrow> bool"    ("_ \<turnstile> _ : _" [50, 50, 50] 50)
 where
-  T_Var: "\<Gamma> \<turnstile>\<^bsub>wf\<^esub> \<Longrightarrow> \<Gamma>\<langle>i\<rangle> = \<lfloor>VarB U\<rfloor> \<Longrightarrow> T = \<up>\<^sub>\<tau> (Suc i) 0 U \<Longrightarrow> \<Gamma> \<turnstile> Var i : T"
+  T_Var: "\<Gamma> \<turnstile>\<^sub>w\<^sub>f \<Longrightarrow> \<Gamma>\<langle>i\<rangle> = \<lfloor>VarB U\<rfloor> \<Longrightarrow> T = \<up>\<^sub>\<tau> (Suc i) 0 U \<Longrightarrow> \<Gamma> \<turnstile> Var i : T"
 | T_Abs: "VarB T\<^sub>1 \<Colon> \<Gamma> \<turnstile> t\<^sub>2 : T\<^sub>2 \<Longrightarrow> \<Gamma> \<turnstile> (\<lambda>:T\<^sub>1. t\<^sub>2) : T\<^sub>1 \<rightarrow> \<down>\<^sub>\<tau> 1 0 T\<^sub>2"
 | T_App: "\<Gamma> \<turnstile> t\<^sub>1 : T\<^sub>11 \<rightarrow> T\<^sub>12 \<Longrightarrow> \<Gamma> \<turnstile> t\<^sub>2 : T\<^sub>11 \<Longrightarrow> \<Gamma> \<turnstile> t\<^sub>1 \<bullet> t\<^sub>2 : T\<^sub>12"
 | T_TAbs: "TVarB T\<^sub>1 \<Colon> \<Gamma> \<turnstile> t\<^sub>2 : T\<^sub>2 \<Longrightarrow> \<Gamma> \<turnstile> (\<lambda><:T\<^sub>1. t\<^sub>2) : (\<forall><:T\<^sub>1. T\<^sub>2)"